ABSTRACT: It is thought that many characteristics of the central parsec of our Galaxy, from Sgr A* to the ``mini-cavity'', are associated with the accretion of ambient gas by a central concentration of mass. Using a 3D hydrodynamical code, we have been simulating this accretion process, in order to realistically model the gaseous flows in the center of our Galaxy. In the most recent simulations, we have taken into account the multi-point-like distribution of stellar wind sources, as well as the magnetic heating and radiative cooling of these stellar winds. As expected, we find that the structure of the flow is significantly different from that due to a uniform medium. We also investigate the possibility that Sgr A* is due to a distributed mass concentration instead of the canonical point mass of a black hole. We discuss the physical state of the accreting gas and how our results suggest that Sgr A* is unlikely to be associated with a ``dark cluster''.